Suppose that three numbers are selected one by one, at

Chapter , Problem 21

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QUESTION:

Suppose that three numbers are selected one by one, at random and without replacement from the set of numbers {1, 2, 3, . . . , n}. What is the probability that the third number falls between the first two if the first number is smaller than the second?

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QUESTION:

Suppose that three numbers are selected one by one, at random and without replacement from the set of numbers {1, 2, 3, . . . , n}. What is the probability that the third number falls between the first two if the first number is smaller than the second?

ANSWER:

Step 1 of 2

The possibility given is that the 1st number is smaller than the 2nd number.

So, the three possibilities are:

1st< 2nd< 3rd

3rd< 1st< 2nd

1st< 3rd< 2nd

The total number of possibilities = 3

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